Question

solve for y and graph the solution.
15 ≥ 3|y + 20|
click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles, click on them.

Explanation:

Step1: Simplify the inequality

Divide both sides of \(15\geq3|y + 20|\) by \(3\).
We get \(5\geq|y + 20|\), which is equivalent to \(|y+20|\leq5\).

Step2: Use the property of absolute - value inequality

If \(|a|\leq b\) (\(b\geq0\)), then \(-b\leq a\leq b\).
Here \(a = y + 20\) and \(b = 5\), so \(-5\leq y+20\leq5\).

Step3: Solve for \(y\)

Subtract \(20\) from all parts of the compound inequality.
For the left - hand side: \(-5-20\leq y+20 - 20\), which gives \(-25\leq y\).
For the right - hand side: \(y+20 - 20\leq5 - 20\), which gives \(y\leq - 15\).

Answer:

The solution of the inequality is \(-25\leq y\leq - 15\). On the number line, we click on the point \(-25\) (filled - in circle) and the point \(-15\) (filled - in circle) to graph the line segment between them.